To cite articles published in the Journal of Artificial Societies and Social Simulation, please reference the above information and include paragraph numbers if necessary

Received: 03-Aug-2003
Accepted: 12-Dec-2003
Published: 31-Jan-2004

Abstract

Discrete agent simulation was used to study the role of reciprocity and normative reputation in the development of mutual obligation in gift-giving societies. Measures of economic and non-economic rewards were tracked over many generations of agents acting within a fixed environment and according to a constant behavioral rule set. Communicating normative reputation enabled potential victims to avoid theft without the necessity of personally experiencing the character of every agent. It also optimized mutual obligation among agents, even among aggressive agents. These results are discussed in the context of theories of positive and negative reciprocity and are related to observations of some hunter-gatherer societies.

Introduction

Reciprocity was a key factor in the social dynamics of many primitive peoples. Numerous ethnographic studies demonstrate that hunter-gatherer peoples developed elaborate and strict rules for sharing, rules that had the effect of optimizing resource use, especially in cultures that lacked storage capacity. For example, the !Kung of the Kalahari hunted in small groups and then shared the results with everyone in the tribe. Villagers in some Polynesian societies collectively gathered food and then distributed it to all of the members of the village. Such customs promoted a degree of social equity that was essential in situations where food collection by individuals was not sufficiently reliable to meet daily needs and where storage was not practiced or practicable. See, for examples, the papers in Gowdy (1998) and the study of Mauss (1990). However, the functionalist argument that hunter-gather peoples gave gifts to assure future economic return should not be overstated. The basic necessities of life were easily obtained in many such societies so that sharing was not required to sustain an individual. There were important non-economic social functions associated with reciprocity, including the establishment of reputation, social prestige, and the creation of a power base for leadership. This paper examines the role of reputation and its communication in simple artificial societies in which there are parallel economic and non-economic reward structures. Particular attention is paid to the development of mutual obligation amongst the members of a society.

Positive reciprocity in its pure form constitutes altruistic giving, generosity without an expectation of return. But, positive reciprocity need not be exclusively altruistic and it is not solely economic in nature. Gift giving can encourage a sense of obligation in the recipient that provides the giver confidence that the favor will be returned. Repeated instances of such sharing engender a sense of mutual obligation among the members of a society and in so doing enhance social cohesion. As noted by Ekeh (1974), "Every social exchange transaction creates social bonds that not only tie one person to another and to society but one segment of society to another." In the case of the !Kung, Yellen (1998) observed that "security was obtained by giving rather than by hoarding, that is, by accumulating obligations that could be claimed in times of need." There are also political motivations for gift giving. Pospisil (1958) stated of Kapauku that "society views its ideal man as a most generous individual, who through the distribution of his fortune satisfies the needs of many people. Generosity is the highest cultural value and an attribute necessary for acquiring followers in political and legal life." In his classic study of the Trobriand Islanders, Malinowski (1984) found that a chief won followers through the distribution of food. Generosity increased the reputation of the giver, so aspiring leaders gave to the point of personal penury. Finally, we note that the motivation to give is not restricted to "primitive" cultures. Mauss (1990) cites the classical Hindu law: "The thing that is given produces its rewards in this life and the next. Here in this life, it automatically engenders for the giver the same thing as itself: it is not lost, it reproduces itself; in the next life, one finds the same things, only it has increased." Ekeh (1974) argues that such considerations are found in modern culture as well.

Trade, the exchange of goods or services of equal value, is conducted in almost all societies. Trade was kept distinct from the gift process in many primitive cultures. While it was deemed unacceptable to deny a gift to one in need, especially within a defined sphere of kinship, haggling was permitted in trade. In environments where the basic necessities of life were plentiful, trade could assume roles other than the purely economic. As Firth (1927) observed, "The exchange takes place in gratification of a complex set of social motives - pride, vanity, ambition, sense of kinship bonds - but on the principle of economic utility there is no 'need' for them to occur." Often, exchanges of little practical utility were conducted and in some cases the items traded were destroyed as part of the process. When trade was introduced into some self-sufficient hunter-gatherer societies the result was a focus on toys, unnecessary clothing, or luxury goods rather than utilitarian tools that would enhance economic productivity. The participants thought that these things enhanced their social prestige. One could argue that such peoples had not yet "learned" economics, but this is precisely the point. They operated within a different value structure, one less rooted in countable material assets and services. In primitive societies non-material rewards played a vital role in exchange, as indeed they did and do in other societies. For example, sacrifices common in many religions might be seen as an attempt to exchange material goods for non-material blessings or an expectation of future well-being.

Negative reciprocity ranges from a passive withholding of an obligatory return gift to the aggressive theft of goods owned by another agent. In contrast to positive reciprocity, there may be a limit to the degree to which the members of a society can practice negative reciprocity. Aggression and theft can benefit a sub-group, but only within a victim population that produces the goods to be expropriated. While hunter-gatherer cultures have, like almost all other societies, demonstrated their capacity for aggression, a point made effectively by Keeley (1996), few societies consist entire of thieves. Some degree of cooperation, or at least some moderation of aggression within a social unit, appears to be vital to all functioning societies.

Reciprocity and reputation are linked in social interaction. An agent's reputation, both at the individual and the social level, determines how that agent will be treated in social exchange. Trust and a sense of mutual dependence are components of positive reciprocity. In trade there is an expectation of payment or exchange of comparable value. In negative reciprocity, bad reputation may lead to the avoidance of aggressive agents even without personal experience of the aggressor.

The value of reputation and the use to which it is put depends on the reward structure associated with social interaction. If there is only one factor involved, the decision calculus may be straightforward. This is the case, for example, in purely economic transactions where action can be optimized to accumulate rewards while minimizing cost. When the reward calculus involves several factors, and when more subjective factors such as individual prestige are involved, the decision process can be more complex. For example, one might think that flight from known aggressors is a low cost way to avoid loss due to theft. However, if the effect of theft is only the loss of easily replaced material goods, and if the result of running away is to avoid desirable social interactions, then the victim may suffer more by running than by enduring the lesser material loss. As the value of the stolen goods increases, or the value derived from social interaction decreases, this calculus will change, but the point remains that non-economic factors could play a significant role in deciding agent actions.

Discrete agent simulation has proven a useful tool for analyzing the effects of behavioral rules in well-controlled computational environments. Several studies have been done to illustrate the benefits of altruistic sharing on social performance. Saam and Harrer (1999) studied simulated populations that followed rules by fiat vs. those that chose the best course of action for each situation. They found that the benefits of normative compliance were sensitive to the social structure in which the individual acted and that social equity was enhanced in those cases where the distribution of goods was most uniform. Jaffe (2002) studied the effect of pure altruism on economic performance. He found that altruism was not optimum for the accumulation of wealth, although it did enhance social equity. Younger (2003) found that clustering in social structures enhanced the opportunity for sharing and in so doing enhanced individual and social performance. This is consistent with the conclusion of Homans (1958), who cited previous work that demonstrated that "the more cohesive a group is, that is, the more valuable the sentiment or activity the members exchange with one another, the greater the frequency of interaction of its members."

This paper extends our previous work (Younger 2003) by investigating the roles of reciprocity and reputation in simple societies containing both economic and non-economic reward structures. We used discrete agent simulation to study the performance of simple societies of agents acting according to a well-defined set of rules governing exchange. Based on these exchanges, agents formed opinions of their fellows, opinions that could be changed as a result of communication with other agents. The thesis of this work is that normative reputation plays an important role in the development of mutual obligation within gift-giving societies. Further, we posit that this mutual-obligation is consistent with greater social equity within those societies.

An extensive literature exists for role of reputation in social exchange. See, for example, the discussion of game-based models in Ridley (1998). Several many-agent simulation studies have examined the role of reputation in normative (rule following) and aggressive (stealing) populations. Castelfranchi, Conte, and Paolucci (1998) found that normative reputation shared among norm-following agents in a mixed population of normative and aggressive agents significantly enhanced the performance of normative agents by redistributing the cost of normative compliance. It was more efficient for agents to share the results of their encounters with aggressive agents than to have each agent learn for itself. Hales (2002) extended this work to the concept of group reputation, wherein experience with one member of an identified group established a reputation for the entire group. Both of these studies contained a purely economic reward structure - strength points gained as a result of the consumption of food. In this paper we add a non-economic reward structure that mimics aspects of positive and negative reciprocity. We examine how the communication of normative reputation affects both economic and non-economic rewards in two simple social structures, one in which agents act independently and one in which they are constrained to function within groups.

In the next section we summarize the method employed in the simulations. In subsequent sections the results are presented and discussed in the context of social theory and in comparison to previous work.

Computational Method

MICROS, the simulation tool used here, used a discrete agent technique wherein a set of agents occupied a fixed landscape and acted according to a predefined set of behavioral rules. A detailed description of MICROS was given in previous papers (Younger 2002; 2003).

An initial group of 20 agents, sufficient to start a population via procreation, was placed in a two dimensional artificial landscape of 20 × 20 squares. Agents had needs for food, sleep, companionship, and activity. Five food centers were placed in the landscape and were replenished at a fixed rate of 20 units per timestep, consistent with a sustainable population of 100 agents. Ten shelters provided agents an accelerated means of satisfying the need for rest. Two of these were designated "home shelters", or villages, where goods collected by the agents were deposited and where the agents had advantages in mating. Material centers, each containing a large (1,000,000 units) and unreplenished quantity of material points, were used as sources of material wealth. Agents moved about the landscape at a rate of one square per timestep to find food, collect materials, interact with one another, and seek knowledge about their environment. Needs for hunger, sleep, companionship, and activity were each increased by one point per timestep. At each timestep each agent acted upon its greatest need. Sleep was the highest priority - an agent died if its need for rest exceeded 100 units. Similarly, an agent died if its need for food exceeded 200 units. An agent could live a maximum of 4000 timesteps and simulations were run for 40,000 timesteps, or ten agent lifetimes.

Action was sequential - only one agent acted at a time. If the needs for food and rest were low, then an agent's decision was whether to seek companionship or to explore the landscape. Neither of these needs were lethal. The need for companionship was satisfied by sharing goods or information with another agent, by mating, or by stealing.

A two dimensional grid was used to mimic a land surface. The boundary conditions on the landscape were reflective - when an agent encountered a wall it turned to another direction. This corresponded to an island geography. A grid of 20 × 20 was found convenient for agent interaction in that, at a movement rate of one square per timestep, agents could traverse the landscape many times during their lifetime and have frequent encounters with other agents, all within a population that was computationally manageable. A sensing range of 2 squares in each direction meant that an agent could not sense the entire environment from one location. Limited field of view is common in forests and other cluttered terrain.

Agent knowledge consisted of knowing the location and status of food centers, material centers, and shelters. Since the quantity of goods at a center changed as a result of agent actions, knowledge was time dependent. For example, food centers could be exhausted by agents eating and taking food back to their home shelters. If an agent knew that a particular food center was empty, it would bypass it and go to another one. Knowledge of the status of the food and material centers was updated either by an agent's own sensation or by communication of more recent information from another agent.

Agents were divided into two categories: sharing (normative) and stealing (aggressive) agents. (In this paper we will use as interchangeable the terms sharing and normative; stealing and aggressive.) A sharing agent could communicate its knowledge of the landscape and share any food and material points that it was carrying with other agents occupying the same location. Stealing agents did not share but stole food and materials carried by agents of lesser strength. While there was symmetry in the sharing and stealing of material goods, there was an asymmetry in the sharing of information. Sharing agents shared information, but stealing agents did not lie, or provide disinformation about the environment or about other agents. Such disinformation would constitute a loss to the victim, in that it might cause the agent to make decisions injurious to itself. However, information was time dependent in that the supplies at the food and material centers were constantly changing. In providing what it thought was incorrect information the stealing agent could, inadvertently, help the victim by supplying more accurate information than already existed in the victim's memory. Also, there were a variety of ways that such disinformation could be provided. We avoided these complexities by not allowing stealing agents to communicate at all. The withholding of information was a form of penalty that was consistent and easy to apply.

An "interaction matrix" tallied the positive and negative effects of agent interaction and was constructed to model the effects of reciprocity observed in some primitive cultures. A unique interaction matrix element coupled each pair of agents. It was increased during sharing or mating and it was decreased by theft. In this sense the interaction matrix was a record of the past adherence of agents to normative behavior and constituted a form of reputation. A summary of contributions to the interaction matrix element is given in Table 1. When an agent received goods or information from another, its opinion of the giving agent increased. So too did the opinion of the giving agent toward the receiving agent. Conversely, when an agent was the victim of theft, its opinion of the thief decreased. Sharing of goods or information only occurred when the giving agent had a zero or positive interaction matrix element with the potential receiving agent. Stealing did not depend on the interaction matrix element connecting thief and victim. Alternate forms of the interaction matrix are possible. We investigated only one plausible model that emphasized the role of gift-giving and social relationships.

Table 1: Contributions to the agent quality factor and the interaction matrix

Agents were divided into male and female. Mature agents of opposite sex connected by interaction matrix elements greater than or equal to zero could mate and produce offspring. Agents were only permitted to mate during the ages of 1000-2000 timesteps. This eliminated the possibility of mating between parents and offspring. Agents did not mate with siblings. The probability of conception in a mating event was 25% and it was increased by 5% if the agents had previously mated with one another and an additional 5% if they were mating at a home shelter. Other factors that affected conception, such as the strength of the parents or their genetic heritage, were not included in this study. The gestation period was 200 timesteps, so a mother could produce a maximum of 5 offspring during her lifetime. There was equal probability that offspring were male or female and normative or aggressive. Offspring remained with the mother for the first 800 timesteps of life to simulate a nurturing period.

A quality factor tracked non-material aspects of agent performance using a value structure designed to mimic that of gift-giving cultures. It did not influence agent decisions but only measured the results of those decisions. The quality factor increased when the agent learned about its environment, shared that knowledge, mated, and when goods were given to or received from another agent. It decreased when the agent was a victim of theft and when the agent was very hungry or tired. A summary of contributions to the quality factor is given in Table 1 and a detailed discussion can be found in Younger (2003).

Agents in MICROS followed a predefined set of rules that remained fixed throughout the simulation. Evolution of behavior was not included in MICROS. Rather, the intention was to examine the effect of a population executing a fixed set of rules over many generations. Such consistency of behavior is suspected to have occurred over millennia in Australian Aborigines, where even patterns of tool fabrication were virtually unchanged over long time periods. However, consistency of behavioral rules does not imply stasis in the population. It was sometimes observed that agent parameters oscillated about mean values with a period of several agent lifetimes as large-scale social trends played out. For example, a stochastic imbalance in the male/female ratio could lead to a temporary slowdown in reproduction, which could cause the buildup of a food surplus in the environment, which in turn caused a population increase followed by overpopulation and famine.

In their simulation of the effect of communicating normative reputation on economic performance, Castelfranchi et al (1998) and Hales (2002) used a simulation scheme that permitted only one agent per square and did not include procreation beyond the immediate replacement of agents who died. Only one agent parameter, strength, was considered and that was dependent on food obtained from the landscape. MICROS allowed many agents to occupy the same location and procreation and family structures were included. Allowing more than one agent to occupy a given location increased the number of agents who could interact with one another. It was not unusual for a single square to contain in excess of 10 agents, more than could interact if only one agent was permitted per square. The agents in MICROS also had a richer range of actions than food consumption through the requirements to rest and to seek companionship. Another difference between the present study and the work of Castelfranchi et al (1998) and Hales (2002) was that the latter allowed normative agents to steal from agents known to be aggressive. In MICROS, normative agents remained normative and never stole.

To enable a closer comparison to Castelfranchi et al (1998) and Hales (2002) we altered the definition of agent strength that was employed in our previous study (Younger 2003). In the simulations reported here, agents started with an initial strength allocation of 100 points. Strength was reduced by one point per timestep, indicative of energy use. Points were added for food consumed. The number of food units stolen was deducted from the victim's strength and added to the strength of the attacker. Since strength only appeared in the calculation of whether an aggressive agent would steal goods from other agents (agents only steal from weaker agents) we did not expect this change to have a significant effect on the simulation. Repeating runs using the new formulation of agent strength and comparing the results to the version in our previous paper verified this. No significant difference was observed. Other than this change, the addition of flight from aggressive agents, and the communication of normative reputation, the method here was the same as was used in Younger (2003).

Normative reputation was communicated in MICROS by averaging the interaction matrix elements of the giving and receiving agents. Since agents act in sequence and not simultaneously, information flow was one-way. Agent i gave information to agent j, but the favor was not returned during that timestep since only agent i was acting. Only normative agents shared reputation. Normative reputations were shared with another agent only when an agent had an interaction matrix element greater than or equal to zero with the receiving agent. The same reputation could be shared many times over, incrementally changing the opinion of the receiver and, by propagating through the population, equalizing the reputation of aggressive agents among normative agents. For example, if agent A had an interaction matrix element of 100 for agent C and agent B had an interaction matrix element of 200 for agent C, then when A conveyed its opinion of C to B the new opinion of B towards C would be (100 + 200) / 2 = 150. If, during its turn, agent B communicated its opinion of agent C to agent A, then A's new opinion would be (100 + 150) / 2 = 125. If the agents remained collocated during the next timestep, another exchange could occur, ultimately leading to convergence of the interaction matrix elements of A and B for C.

It was possible for normative agents to have a positive interaction matrix element with an aggressive agent who had not yet exhibited its aggression through theft. Theft could only occur when an agent was carrying something and this condition was extant for only a fraction of the total life of the agent. At other times the normative agent might mate with the aggressive agent, forming a positive interaction matrix element. If this positive reputation was shared with another agent it could change the sign of the receiving agent's opinion of the aggressive agent from negative to positive. Thus an agent who had been a victim of an aggressive agent could have its negative impression erased. Conversely, a positive reputation could be changed through interaction with other agents who had negative experiences with the aggressive agent. Note, however, that the effect of normative reputation, as represented in the interaction matrix, was binary. Decisions were based only on whether the interaction matrix element was positive or negative, not on its magnitude.

An option was included to allow agents to flee from the approach of an agent with whom it had a negative interaction matrix element. If an agent sensed the presence of such an agent then it interrupted any current activity and moved away during its active timestep. Flight was a positive response to reputation. Otherwise, an agent could only decline to share or mate, a passive response to recognized aggressive character.

A parameter called the obligation factor was introduced to monitor the degree of mutual obligation within the society. The obligation factor for a specific agent was defined as the sum of all of the interaction matrix elements of other agents for that agent. Since the interaction matrix element was a function of agent interaction, affected by mating, sharing, and theft, this sum represented the net contribution of an agent toward its fellows and, by inference, the obligation incurred by them. The obligation factor represented the degree of esteem in which the population held the individual. Since it was a function of reciprocity, it was analogous to the type of social obligation found in Polynesian cultures. To mimic the role of reciprocity in the power structure of hunter-gatherer cultures, the obligation factor was the major determinant in the selection of a leader. Leaders were chosen based on the sum of the obligation factor and an additional "leadership factor" defined as the product of a random number in the range 0-1 and the total population. The purpose of the leadership factor was to include an innate personal characteristic in the definition of the leader.

MICROS was capable of simulating several simple social structures including families (restricted to monogamous couples and their offspring) and the assignment of agents to a particular home shelter to which goods collected under instruction of a leader were returned. In scenarios with family structures, once two agents mated they remained collocated for the remainder of their lives. Family relationships and leadership encouraged the clustering of agents and, by so doing, increased social interaction and the impact of positive and negative reciprocity.

The parameters chosen for the simulation were intended to be a compromise between realism and computational efficiency. A principal factor in their selection was the desire to create a sustainable society. The agent's first priority was to satisfy physical needs. They needed sleep more urgently than food, which was also intended to represent the need for water. After physical survival was assured there was a need for companionship, a stimulus for social interaction. If all of these needs were met, the agent explored the landscape as something to do, a need for activity. The lifetime of the agents was intentionally short since, for such a small landscape, after 1000 - 2000 cycles each agent knew all of the features of the landscape. A new group of agents, produced through procreation, improved the statistics of the simulation within a fixed physical environment. One could certainly introduce other needs in more complex models, such as the need to worship, or a need to remain in extended family units.

A number of test cases were done to investigate the sensitivity of the results to the parameters of the simulation. First, runs were done with a length of 100,000 timesteps, or 100 agent lifetimes, to test whether the artificial society had come to equilibrium. The results were consistent with those presented below. In another variation, a run was made for a human lifetime (70 years) where each timestep corresponded to one hour. After scaling for the increased time that an agent had to accumulate quality factor and other points, the results were consistent with those for smaller runs. Other runs were made with food supplies consistent with maximum populations as high as 500 agents. The results were qualitatively similar to those of the smaller runs, but detailed comparison was not possible since the density of agents was higher for our fixed environment. Enlarging the landscape to keep agent density constant introduced additional complications, such as the time required to traverse the landscape. Other distributions of food and material centers were studied, with no noticeable effect on the results. To investigate the sensitivity of the results to agent characteristics, a set of parameter variations was conducted. Changes were made to three groups of parameters: agent lifetime, the combination of sensation range, movement rate, and carrying capacity, and the combination of the need for food and the need for sleep. These may be categorized, respectively, as agent longevity, agent capability, and agent endurance. Each group of parameters was changed by 50% and the results noted. Increasing the lifetime of the agent improved social stability as there were fewer turnovers in the population. Increasing agent capability had a relatively small effect on the simulation since the agents existed in a resource constrained environment. The ability to carry more or move faster was of little benefit when the aggregate amount that could be shared or carried was determined by the environment. Increasing the endurance of the agents by 50% actually led to a less robust society. A higher threshold for hunger allowed an agent to go longer without eating, but when it did go to a food center it would consume so much food that it could deplete the center. Other agents visiting the center would then be unable to satisfy their own hunger. Reducing agent endurance forced agents to spend more time on food collection since they had to eat more often, placing additional stress on the population. The key to a sustainable society was the avoidance of oscillations in environmental or agent parameters. We chose agent parameters that ensured that most populations survived, but which created enough stress on the agents to illuminate the effects of reciprocity and reputation. Indeed, a characteristic of long-lived hunter-gatherer societies was that they did achieve a sustainable state.

Alternate formulations of the quality factor and the interaction matrix are possible. However, the quality factor is solely a measurement of the results of agent decisions - it does not influence agent behavior. Sharing and stealing are the dominant contributions to the quality factor. The maximum contribution of mating is 100 (first mating) + 5 (maximum number of pregnancies) × 20 (contribution per pregnancy) = 200. Most quality factors were of the order of 1000 or more, so sharing and stealing were the dominant contributions. Changing the percentage contribution of goods shared or stolen would change the quantitative value of the quality factor but would not change the qualitative results of this paper. More significant changes to the composition of the quality factor, such as rewarding theft vs. sharing, would be interesting to study but do not reflect the role of reciprocity in most primitive cultures. The interaction matrix and the resulting obligation factor could also be changed to reflect alternate reward structures for social interactions. Reducing the positive contribution from sharing and mating while increasing the negative effect of stealing would make it more difficult for agent reputations to be changed. The limit of this variation, making any stealing event so damaging to agent reputation that no recovery is possible, will be discussed in the next section.

We extended the notation used in our previous paper to include indicators for the communication of normative reputation and flight. A six-character string summarized the features included in each scenario. The label MHFLNT refers to a MICROS run (M) with home shelters (H), family relationships (F), leadership (L), communication of normative reputation (N), and flight (T) and is the most sophisticated social model here simulated. When a feature is not present a zero occupies its position. Hence, MH0000 corresponds a run with home shelters but without family structures, leadership, the communication of normative reputation, or flight. As a comparison case, we calculated two scenarios in which agents maintained no information on normative reputation. These cases were designated "No rep" in the results table.

Finally, we note that there was no agent "interest" or "intention" in MICROS. Agents had no "expectation of future interactions", as discussed by Macy and Willer (1998), that would form the basis of rational decisions about future events. They existed in the moment and acted according to a fixed set of rules. The value in this approach was precisely that it started from a clear set of assumptions of agent behavior and then followed those assumptions to their logical conclusions. One can only say of the simulations that if agents acted according to this set of rules then a specific result was obtained.

Results

We began by reproducing, in so far as was possible within the MICROS computational scheme, the results of Castelfranchi et al (1998). We calculated a population of 60 agents for one lifetime (4000 timesteps) in the MH0000 scenario. Mating was not allowed. An equal mix of normative (sharing) and aggressive (stealing) agents was modeled. In this series only, the interaction matrix element of the victim for the aggressor was reduced by 1,000,000 points for each theft, making it impossible for the attacker's reputation to be changed by subsequent interaction. Results averaged over 100 runs, shown in Table 2, are qualitatively similar to those of Castelfranchi et al (1998): normative agents had lower strength than aggressive agents since the former only suffered from theft whereas the later benefited. The effect of sharing normative reputation was to improve the strength of normative agents since they could avoid aggressive agents without paying the cost of experiencing their aggressive behavior.

Table 2: Results for a simulation of 30 sharing and 30 stealing agents acting for 4000 timesteps. One theft permanently set the character of the stealing agents. Standard deviations are given in parentheses. Castelfranchi et al (1998) used a different method for tracking agent strength, but the results are qualitatively similar in that normative agent strength increased while aggressive agent strength decreased upon the communication of normative reputation

The major part of our study involved simulations that used the method and parameters described in the preceding section i.e. ten lifetime runs with a sustainable population of 100 agents. The results are given in Table 3. They represent averages over five runs. For the case of no communication of normative reputation and no flight, these results are comparable to those of Younger (2003). The new definition of strength, only a factor in deciding whether theft occurred, did not significantly influence the results. We first present a view of the overall effect of reputation, its communication amongst agents, and flight from aggressors. After that we will discuss each of the significant agent parameters in detail.

We begin with the simplest scenarios, those based on the MH00 model of agents acting as individuals, without family structures or leadership. A comparison of the MH0000 (No Rep) and MH0000 scenarios shows that normative reputation acquired through individual experience had a small but beneficial effect on the strength of normative agents. Sharing rates were slightly higher in the scenario with reputation and stealing rates were slightly lower, an expected result of the role of reputation in influencing agent actions. When agents acted independently, the probability of a repeat theft by an aggressive agent on a given normative agent was small, so individually developed knowledge of normative reputation was of limited value to the normative agents. While the average strength of sharing agents was higher when the agents remembered normative reputation, their quality factor was slightly lower, an illustration of the opposite effects that normative reputation can have on material and non-material performance measures. This effect will be discussed at greater length below.

When flight from known aggressive agents was added to MH0000 to form the MH000T scenario, the quality factor for aggressive agents dropped by almost a factor of three, indicative of the effect of ostracism of the aggressive agents by the normative agents. The sharing rate, the average number of sharing events per normative agent per timestep, increased substantially as normative agents had greater opportunity to share goods with other agents, goods that were not lost to theft. However, more normative agents carrying goods did present more targets to the aggressive agents, so there was a slight increase in the rate of theft. The strength of normative agents went down as their attempts to find and transport food were frequently interrupted by flight from aggressive agents.

Next, we consider what happened when the communication of normative reputation was added to MH0000 to form the MH00N0 scenario. In this case, the ratio of agents who died of old age to those who died of hunger increased slightly but the strength of normative agents decreased slightly. More agents lived the maximum lifetime but they did so with lower material strength. The quality factor of normative agents increased by a few percent but their obligation factor more than tripled. The quality factor for aggressive agents remained the same but their obligation factor increased by almost a factor of six. The communication of normative reputation among normative agents was important in allowing agents to develop mutual obligation while minimizing the possibility of negative interactions with aggressive agents. It even benefited aggressive agents by occasionally changing the reputation of an aggressive agent from negative to positive and allowing that agent to benefit from social interactions where there was no opportunity to steal. However, such a reputation change could still have negative effects on the normative agents, as reflected in a 10% increase in the stealing rate. When a normative agent was carrying something, an aggressive agent would steal it. The sharing rate remained constant, as normative agents shared among one another.

When flight was added to the communication of normative reputation to form the MH00NT scenario, the increase in the quality factor of the normative agents found in the MH00N0 scenario was erased and there was a slight improvement in agent strength. Normative agents fled from known aggressive agents, forgoing social interaction but also forgoing the possibility of theft and a loss to their strength. The increase in the obligation factors remained.

The addition of social structure via family relationships and leadership led to a different pattern. The age/hunger ratio was much higher in the MHFL00 scenario than it was in the MH0000 scenario. This result was discussed extensively in Younger (2003) and was due to increased opportunities for sharing within clusters of agents. Conversely, individual agent strengths were lower when agents acted in social clusters since there were more opportunities for stealing within the social unit. In this case sharing and stealing played complimentary roles - sharing distributed food among the normative agents and stealing allowed aggressive agents to take what they needed from collocated family members. The fact that the age/hunger ratio was higher with social clustering suggests that the benefits of sharing in creating social equity outweighed the damage done by theft. Obligation factors were much higher in the case of social clustering.

When individually learned normative reputation was added to the MHFL00 No
Rep case to form the MHFL00 scenario the strength of normative agents
improved but the age/hunger ratio decreased. Sharing and stealing rates
remained roughly the same with and without memory of reputation. Normative
agents did not share with known aggressive agents, increasing the amount
retained within the normative subpopulation.

When flight was added to MHFL00 to form the MHFL0T scenario, the strength of
normative agents improved but their quality factor decreased. Normative
agents protected their food from theft, but gave up the opportunity to share
that would have contributed to their quality factor. The quality factor of
the aggressive agents decreased by more than a factor of three. The
obligation factor was not significantly influenced by flight. The sharing
and stealing rates both decreased slightly as normative agents avoided
aggressive agents and also normative agents who might be constrained to
travel with those aggressive agents. Such normative agents were no longer
opportunities for sharing. Since family members were required to remain
together, even when some of them were aggressive, theft could occur within
family units, hence the maintenance of a substantial rate of theft. Sharing
rates were always higher in the scenarios with social clustering.

When agents communicated normative reputation in the MHFLN0 scenario, the
age/hunger ratio increased slightly compared to MHFL00. Agent strength and
quality factors were about the same in both scenarios. However, the
obligation factor of normative agents increased by almost a factor of four.
For aggressive agents the increase was even greater, more than a factor of
five. This happened even though the sharing and stealing rates remained
about the same as in the no-communication scenario. Aggressive agents could
benefit by having the negative effects of theft overwritten by the
communication of positive reputations gained through mating with other
agents. It is interesting that the communication of normative reputation
caused aggressive agents to lose (materially based) strength points but gain
(non-material) obligation factor points, thereby improving their integration
into society through mutual obligation.

Adding the communication of normative reputation to MHFL0T to form the
MHFLNT scenario decreased the age/hunger ratio but left agent strengths
relatively constant. It increased the quality factor, especially for
aggressive agents. The obligation factors of both normative and aggressive
agents were increased to levels almost as high as those of the MHFLN0
scenario. Mutual obligation was optimized when normative reputation was
communicated. While the material equity within the society, as measured by
the age/hunger ratio, decreased somewhat, the degree of mutual obligation, a
measure of social cohesion, increased significantly.

We now turn to a detailed analysis of the effect of communicating normative reputation and flight on each of the significant agent parameters. Sharing and stealing rates were higher for the MHFL-based scenarios than the MH00-based scenarios due to the enhanced clustering in scenarios with social structure. There were more opportunities for interaction in scenarios with family structure and leadership. The sharing and stealing rates were less influenced by the communication of normative reputation than by social structure. A stealing rate of 0.003 per agent per timestep, typical for the MH00-based scenarios, corresponded to 0.003 × 4000 = 12 thefts per lifetime per aggressive agent. With equal populations of sharing and non-sharing agents this rate suggests that each agent would either perpetrate or suffer one or more thefts during its lifetime. The probability of a second attack on an individual by the same aggressor was small. The sharing rate was higher than the stealing rate in the MHFL-based scenarios. This was because a normative agent shared equally with all other agents at its location but an aggressive agent could steal from only one agent at a time.

The rate of flight was several times greater than the rates of sharing and stealing. The most probable interaction between an aggressive and a normative agent occurred when the latter was not carrying anything. There was nothing to lose from theft, but the reputation of the aggressor still initiated flight. The rate of flight was not sensitive to social context but it was very sensitive to the sharing of normative reputation. It was lower when normative reputation was communicated than when each agent had to establish reputation on its own. This may seem counterintuitive - one might expect flight to be more likely when the reputation of aggressive agents was more widely disseminated. However, since normative reputations were averaged during the communication process, it was possible for positive reputations to outweigh the negative impressions of past victims of aggressive agents, allowing aggressive agents to approach and steal from normative agents.

Two parameters monitored the physical well being of the agents: the age/hunger ratio and the strength of the agents. As was found in our previous study, the age/hunger ratio was sensitive to the social scenario. It was higher in the MHFL-based scenarios than the MH00-based scenarios. Family structure and leadership each promoted clustering of agents and increased the opportunity to distribute food. The communication of normative reputation had a relatively small effect on the age/hunger ratio in social structures since most sharing occurred in family units and since aggressive family members, who did not benefit from sharing, could steal what they needed.

Normative agent strength was always negative - an indicator that they had been victims of theft. Since strength depended on food collected, normative agents could only increase their supply by collecting it themselves and by receiving it from other sharing agents. Aggressive agents collected food themselves and stole food from others. Whereas normative agents shared what they were carrying equally among all agents present at their location, aggressive agents took everything that a victim was carrying. Since there were more opportunities for theft to occur within a social unit, the strength of normative agents was lower and the strength of aggressive agents was higher when there was enhanced clustering. Normative reputation formed by individual agents in the MH00-based scenarios improved the strength of normative agents. When this normative reputation was communicated to other agents this gain was erased although there was a slight increase in social equity as measured by the age/hunger ratio. Normative agents lived longer, but with lower strength. For the MHFL-based scenarios the situation was more complex. Increased
social contact in family units and while following the instructions of local
leaders led to a slight increase in the age/hunger ratio but a slight
decrease in normative agent strength.

The non-material parameters included the quality factor and the obligation factor. Both of these were higher for normative agents than for aggressive agents, a result of the importance placed on sharing in the construction of these factors. In scenarios without flight, the difference in quality factors between normative and aggressive agents was relatively small, on the order of 25%. In the case of MH000T and MHFL0T, i.e. no communication of normative reputation but flight enabled, the quality factor of the normative population was more than a factor of two greater than that of the aggressive population. Without the communication of normative reputation there was no opportunity for a negative opinion to be changed and thus there was no ability for the quality factor of the aggressive agent to benefit from future interactions with the normative population.

The obligation factor, the summation of interaction matrix elements involving a given agent, further highlighted this effect. Aggressive agents did not share and hence accumulated points in their obligation factors only through mating. Obligation factors for aggressive agents were much higher when normative reputations were communicated than when they were not since there was the possibility that their reputations could be changed after they had stolen. The lack of social clustering and the permanence of reputation in the cases where reputation was not shared severely reduced the obligation factor of aggressive agents. The obligation factor of normative agents was highest in the MHFL-based scenarios since social clustering promoted sharing and mating between normative agents.

Discussion

The thesis of this work was that normative reputation plays an important role in the development of mutual obligation within gift-giving societies and that this mutual-obligation was consistent with greater social equity within those societies. We found that the communication of normative reputation significantly increased the mutual obligation among both normative and aggressive agents. Mutual obligation was found to decrease when agents fled from potential aggressors, suggesting that the damage done by theft was less than the lost opportunity for social interaction. The highest degree of mutual obligation occurred in social units, which also had the highest degree of social equity, as measured by the fraction of agents who lived into old age.

The manner in which normative reputation was established and shared was important. The normative population permanently ostracized an aggressive agent if its reputation was set once and for all upon the first instance of its aggression. If reputation was constructed from shared positive and negative experiences with aggressive agents, there was the possibility that negative impressions could be changed, allowing the aggressive agent to participate in future positive interactions with normative agents.

Kollock (1993) studied various accounting systems in social exchanges that contained random noise and found that social performance was optimized when agents "forgave" offenses some of the time. There was no noise in the present study, but the value of changing opinions about aggressive agents, simulated by changing the sign of the interaction matrix element, was the same. Massive non-normative behavior leads to very low age/hunger ratios and quality factors, as was found in our previous study (Younger 2002). But, in a 50/50 mixed population the age/hunger ratio was still favorable with frequent interactions between normative and aggressive agents.

It is interesting to compare these results with observations of hunter-gatherer societies in which gift giving was prominent. The number of deaths by starvation decreased in our scenarios when agents shared and when that sharing was optimized in social clusters. This is consistent with the functionalist argument that sharing promoted social equity in primitive societies by a more even distribution of food and resources. However, gift giving in primitive societies was motivated by more than the promise of future economic return. Sharing was expected. It demonstrated commitment to the social unit, established ties of obligation, and engendered a sense of belonging to society. We simulated the non-economic value of sharing in primitive societies by the interaction matrix and its amalgam, the obligation factor. We found that the obligation factors of sharing agents were much higher than those of stealing agents. The obligation factor was much higher in social clusters where sharing was most effective, than when agents acted on their own. In both social scenarios, it was maximized when normative reputation was communicated. The communication of normative reputation helped the giver focus its generosity on those most likely to be reciprocal in the future. Communication of positive impressions of an aggressive agent, impressions gained as a result of mating with other agents, was important in the enhancement of its obligation factor. A comparable phenomenon is found in primitive societies where behavior was integrated over many actions. Seldom was an individual permanently ostracized for one negative action, but if such behavior became persistent then the aggressive agent would suffer as a consequence. In the political realm, prospective leaders in some Polynesian societies gave gifts to people whose loyalty they sought. It was the obligation felt by the people to the chief that gave the leader his authority (Firth 1927).

This paper investigated only one plausible non-material reward structure inspired by some gift-giving hunter-gatherer cultures. The study of alternate non-material reward structures remains a fruitful area for research. If sharing was poorly rewarded and a premium put on demonstrating personal strength through theft, then quite different results would be obtained. However, such a brutish society might well be short lived. Violence, a more serious form of aggression in which damage was done to the victim in addition to the loss of goods, could also be added to the simulation.

Government Report Disclaimer

This report was prepared as an account of work sponsored in part by an agency of the United States Government. Neither the Regents of the University of California, the United States Government nor any agency thereof, nor any of their employees make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the Regents of the University of California, the United States Government, or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the Regents of the University of California, the United States Government, or any agency thereof.